From the EP-A-1 231 116 a gas bag of the type initially mentioned is known, which has a ring-shaped chamber which is to be inflated, which surrounds an indentation. The indentation extends from the front wall of the gas bag, facing the vehicle occupant, centrally towards the rear. The deepest point of the indentation is formed by a fabric piece which is fastened permanently to the gas bag module and therefore is not moved towards the occupant during unfolding. In the inflated state of the gas bag, the closure piece, which is fastened to the gas bag wall, covers the opening of the indentation, so that the vehicle occupant is prevented from penetrating into the indentation.